a. Several years ago, Castles in the Sand Inc. issued bonds at face value of $1,

Question

a. Several years ago, Castles in the Sand Inc. issued bonds at face value of $1,000 at a yield to maturity of 8.4%. Now, with 7 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 15%. What is the price of the bond now? (Assume semiannual coupon payments.) (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. Suppose that investors believe that Castles can make good on the promised coupon payments but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 90% of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Explanation / Answer

For Semi Annual Coupon Payments Price of Bond = [C [1 - (1+r)^-2t] / r] + [F / (1+r)^2t] C - Coupon Payment - $84 ( as at issue bond was issued at face value with YTM at 8.4%) r - YTM - 15% F - Face Value - $1000 t - Years - 7 Price = [42 * [1 - (1.075^-14)/0.075] + [1000 / 1.075^14] = 356.54 + 363.32 = $719.86 b 719.86 = [42 * [1 - (1+r^-14)/r] + [900 / (1+r)^14] Solving for r at 7% we get, Price = $716.3454 Solving for r at 6.95% we get, Price = $719.7405 Solving for r at 6.90% we get, Price = $723.1571 So Expected YTM at 90% Maturity Value will be 6.95% * 2 = 13.90%

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